Question

Erica opened a savings account and deposited $200.00 as principal. The account earns 10% interest, compounded annually. What is the balance after 6 years?
Use the formula A=P (1+r/n)^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

Answer 1

To calculate the balance after 6 years for Erica's savings account, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) is the balance after time \( t \),
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the annual interest rate (as a decimal),
- \( n \) is the number of times interest is compounded per year,
- \( t \) is the number of years.

Given the information:
- \( P = 200.00 \)
- \( r = 10\% = 0.10 \)
- \( n = 1 \) (interest is compounded annually)
- \( t = 6 \)

Now we can substitute these values into the formula:

\[
A = 200 \left(1 + \frac{0.10}{1}\right)^{1 \times 6}
\]

This simplifies to:

\[
A = 200 \left(1 + 0.10\right)^{6} = 200 \left(1.10\right)^{6}
\]

Next, we calculate \( (1.10)^{6} \):

\[
(1.10)^{6} \approx 1.771561
\]

Now multiply this by the principal:

\[
A \approx 200 \times 1.771561 \approx 354.3122
\]

Finally, rounding to the nearest cent, the balance after 6 years will be:

\[
\boxed{354.31}
\]